The engaged couple, who were eliminated back-to-back during weeks six and seven of the dance competition show, stepped out to the 24th Annual Race to Erase MS Gala at The Beverly Hilton in Los Angeles on Friday, marking their first official date night since welcoming their first child, son Shai, in January.

"We've been in baby land. I was so looking forward to tonight," Murgatroyd, 30, told ET's Lauren Zima on the red carpet. "I've been preparing hair and makeup and dresses for, like, I don't know, a couple of weeks getting ready, and then the worst thing happened!"

"My dress broke," she explained. "My whole zipper, as Maks was doing me up, just went [ripping sound]. So, he actually sewed me into this tonight!"

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Chmerkovskiy chimed in, telling ET, "First I fixed the zipper, we did it again, and then it broke again. We found out where the problem is, and so, I'm not really sure that was meant to be so good -- I think it was just an accident!"

"He did such a good job," praised Murgatroyd, who confirmed her fiancé knows how to sew. "From the dancing world, we're with our partners. Back in the competition days, we all had to know how to sew, so, yeah!"

The blond beauty admitted she was just "happy" to be walking the red carpet, because she contemplated staying home after the minor fashion mishap.

"It was sad!" Chmerkovskiy said. "I looked at her and she was like giving up on going. But I was like, 'No, we got ready!' And I think she deserves a night out, for sure. You know, I didn't want to leave [the] baby though."

"We would plan on going out before, but then like half an hour to 45 [minutes later], 'You sure you want to go?' 'No, let's just stay in.' 'OK, good,'" he continued.

Wardrobe malfunctions aside, Chmerkovskiy and Murgatroyd appeared to be having a blast at the star-studded gala. The charity event touched home for the duo, who said they have friends who suffer from multiple sclerosis.

"We know first-hand what it does to people and how debilitating it is," Chmerkovskiy explained. "The fact that Nancy [Davis] made this -- in this town, it's hard to make an event prominent, and this is one of the premiere events outside of the Oscars, Emmys, industry standard sort of things. It's one of the biggest and one of the most successful."

"It's a very special event," added Murgatroyd. "We know Nancy personally. She's a great friend of ours, and she's been doing this for so long that it's such a successful event. It raises so much awareness for MS. We couldn't help but come out."

Also in attendance was Murgatroyd's season 24 partner, Nick Viall, who brought his fiancée, Vanessa Grimaldi. Like the new parents, the Bachelor couple also considered the gala a date night.